Search
 
 

STATICS - CASE STUDY SOLUTION

    Normal Propeller (F1)


Normal Propeller Force Components
 

With the x-y-z axes oriented as shown, the direction of the normal propeller is defined by the spherical angles θ and φ:

     θ1 = 175o
     φ1 = 90o

The magnitude is F1 = 1000 lbs. The cartesian components can be calculated by,

    F1x = F sinφ1 cosθ1
         = 1000 sin90 cos175 = -996.2 lb
    F1y = F sinφ1 sinθ1
         = 1000 sin90 sin175 = 87.2 lb
    F1z = F cosφ1
         = 1000 cos90 = 0 lb

Vector F1 can be written in Cartesian notation as

     F1 =-996.2i + 87.2j + 0k lb

     

  Bent Propeller (F2)


Bent Propeller Force Components


Summing Components 

 

For the bent propeller, the spherical angles are more difficult to find but can be found from geometry. The animation at the left shows how to find these angles. They are,

     θ2 = 200o
     φ2 = 80.59o

The magnitude F2 is given as 1000 lb. The component magnitudes are

    F2x = F sinφ2 cosθ2 = -927.0 lb
    F2y = F sinφ2 sinθ2 = -337.4 lb
    F2z = F cosφ2 = 163.5 lb

Vector F2 can be written in Cartesian notation as

     F2 =-927.0i - 337.4j + 163.5k lb

Next, add F1 and F2 to get the total force on the boat.

     FT = F1 + F2

         = -1923.2i - 250.2j + 163.5k

 


Angles for F2   
     
   
 
Practice Homework and Test problems now available in the 'Eng Statics' mobile app
Includes over 500 free problems with complete detailed solutions.
Available at the Google Play Store and Apple App Store.